Modeling the Growth and Size Distribution of Human Pluripotent Stem Cell Clusters in Culture

Culturing stem cells for clinical applications requires standardized protocols. Bench-scale experiments with hPSCs result in growth of cell clusters under various culture conditions. Mathematical models of cluster size distributions can help to identify plausible growth laws.

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A recently published paper (Bulletin of Mathematical Biology (2024) 86:96) combines previously published experimental data with mathematical models. The data for clusters of stem cells is used to fit mathematical size-distribution models, and to identify plausible underlying growth laws.

This paper arose from an initial project carried out by the first two authors in a graduate course taught by LEK at the University of British Columbia in 2022. At initial stages, the co-first authors, Tharana Yosprakob and Alexandra Shyntar (both graduate students at the University of Alberta) learned how to model and simulate hyperbolic PDEs that describe population size distributions. At the time, Dr. Diepiriye G. Iworima was a PhD candidate at UBC, investigating numerous culture conditions. Fortuitously, her participation (in 2020) in a previous iteration of the same graduate course provided a vital link between data she was developing and the modeling topic for this paper. 

Between those first steps and the eventual paper, much learning had to happen (not least of it, by me, the course instructor). We had to tackle PDEs with tricky boundary conditions, possible variants with clusters breaking and fusing, and a variety of conjectures about how each cluster's size affects its growth rate. Much of the initial theoretical work was eventually replaced by simpler, more pragmatic descriptions of the process when the data was available to be analyzed. 

Then, our goals switched, to finding a method to optimize parameter fits, and to weed out poor models in favour of those that were more plausible. This stage brought new challenges, and a realization that more numerous time-samples could have resolved competing models better. Eventually, we found that a logistic-type growth rate (where clusters grow to a preferred size) appears to be adequate.

Much of the methodology in our paper is well-known (though not, at initial stages, to us). It was, indeed, a learning experience. I am grateful to the young scientists for persevering, and to two extremely patient and helpful reviewers that made valuable suggestions along the way. 

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